Congressional Republicans want nothing to do with Vladimir Putin — and some hope President Donald Trump yanks his invitation for the Russian president to visit Washington this fall.

“I’m not sure that’s such a great idea at this point,” Sen. Pat Toomey (R-Pa.) said in a Monday interview. “Putin has proven to be a very hostile actor with respect to the United States, and so I would prefer that he be kept at an arm’s length until his behavior improves.”

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Senate Majority Whip John Cornyn (R-Texas) sounded a similar note on Monday: “I’m just expressing my preference that it be put on the back burner," he said.

Toomey and Cornyn said out loud what most in the GOP are thinking. But many Republicans otherwise eager to spurn Putin, particularly after Trump’s cozy meeting with the Russian leader in Helsinki last week, aren’t ready to cross their party’s leader by prodding the White House to roll the welcome mat back up.

That leaves Republicans in a rhetorical bind as the White House takes further steps to schedule a second Trump-Putin meeting in the U.S. capital this fall. They want Trump to think twice about the visit, or at least impose conditions that would keep Putin at bay, but they also want to preserve his presidential prerogative to keep a dialogue open.

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Sen. Orrin Hatch (R-Utah), a Trump ally who raised eyebrows last week with his subtle criticism of the first Putin meeting, said he has “mixed emotions” about a follow-up visit.

“I don’t particularly want to see a grand ceremony for Putin, but I don’t have any problem with the two leaders sitting down and hopefully having a better discourse than they’ve had until now,” Hatch told reporters, adding that “I do hope the president rethinks what he said” in Helsinki.

"It's good that we're talking ... he just has to be properly prepared to ensure that in private and in public we are being clear and consistent about our concerns. Otherwise the relationship can't get better," said Sen. Rob Portman (R-Ohio).

Republicans "have serious concerns" with the still-unclear status of U.S.-Russia talks after the first summit, Portman noted. "There's a long list of them."

Jeff Flake (R-Ariz.), one of Trump's sharpest foreign policy critics, offered Trump specific advice ahead of a potential second sit-down with Putin. "It's good to talk to our adversaries, but ... if there's going to be a meeting, there ought to be others present," Flake told reporters.

Even Cornyn, who subtly nudged Trump to scrap the idea of a Putin invitation, said, “The president can do what he wants to do."

Senate Majority Leader Mitch McConnell (R-Ky.), a longtime Russia hawk who is considering teeing up fresh action on sanctions against Putin in the coming weeks, made his position clear. "There is no invitation from Congress" to the Russian president, McConnell spokesman Don Stewart said.

But that's not stopping Democrats from continuing to pounce as their opponents struggle over whether to repudiate Trump’s overtures to Putin. Senate Minority Leader Chuck Schumer (D-N.Y.) prodded the GOP on Monday to do more than send “disappointed tweets” about the chummy posturing in Helsinki, where Trump cast doubt on Russia’s interference in the 2016 election before somewhat attempting to walk back his comments.

“It is not hyperbolic to say that last week may have been one of the worst weeks in American foreign policy in recent memory,” Schumer said on the floor.

Some Republicans were clearly chafing at the prospect of another week of Russia questions distracting from their push to confirm Supreme Court nominee Brett Kavanaugh and bipartisan progress on funding the government.

Missouri Sen. Roy Blunt, the GOP Conference vice chairman, raised his hands over his head, chuckled and told a reporter to review his previous statements about Putin when asked about the second meeting Trump is planning.

Whether the rest of the GOP likes it or not, Trump is ensuring that they'll face ongoing questions about his efforts to defrost relations with Putin. Trump's national security adviser, John Bolton, is expected to meet with Russian counterparts next month, White House press secretary Sarah Huckabee Sanders told reporters on Monday.

Still, while the prospect of a Putin meeting ahead of the midterm elections might be tantalizing to Democrats, no date or formal invitation has emerged.

And others in Trump's party want to give the president the benefit of the doubt to pursue areas of cooperation with Russia despite its electoral sabotage efforts, which director of national intelligence Dan Coats recently warned are already revved up ahead of November.

"Let's not second-judge a guy who's proven to be a pretty good negotiator," Sen. Jim Inhofe (R-Okla.) told reporters.

Sen. Mike Rounds (R-S.D.) observed that Trump "follows very closely what people think about" his decisions. "I don't think he appreciated the public sentiment about what he was trying to do in the first [meeting], and I think he'll learn from that."

Secretary of State Mike Pompeo is certain to face tough questions from both sides of the aisle when he testifies Wednesday in the Senate Foreign Relations Committee, with senators seeking more details about any U.S. commitments Trump made in his meeting with Putin.

But for now, only a few Republicans are ready to follow Cornyn and Toomey in publicly putting Trump on notice about bringing Putin to Washington.

"It's how you go about doing it. Do you put on a great big state dinner or anything else like that? I mean, he's not a friend," said Sen. Ron Johnson (R-Wis.), who visited Moscow and supports dialogue with Russia. "They've got 7,000 nukes. I'd rather be talking to them and have some kind of relationship. I don't have a great deal of expectations."